A steamboat is moving at velocity `v_0` when steam is shut off. It is given that the retardation at any subsequent time is equal to the magnitude of the velocity at that time. Find the velocity and distance travelled in time `t` after the steam is shut off.

A particle starts from rest and has velocity kt after time t. The distance travelled in time t is-

The deceleration exerienced by a moving motor blat, after its engine is cut-off is given by dv//dt=-kv^(3) , where k is constant. If v_(0) is the magnitude of the velocity at cut-off, the magnitude of the velocity at a time t after the cut-off is.

If velocity is depend on time such that v = 4 – 2t. Find out distance travelled by particle from 1 to 3 sec

A particle is moving on X- axis. Its velocity time graph is given in the figure. Find distance travelled by the particle in 5 sec .

The acceleration. If v_(0) is themagnitude the engine is cut off, is given by (dv)/(dt) =- k v^(2) , wher (k) is a constant. If v_(0) is the magnitude of the velocity at cut off, find the magnitude of the velocity at time (t0 after the cut off.

A particle moves with an initial velocity V_(0) and retardation alpha v , where alpha is a constant and v is the velocity at any time t. total distance covered by the particle is

The retadation experienced by a moving motor boat after its, engine is cutoff at the instant t is given by a=-kv^4,where k is is a constant. If v_0 is the magnitude of velocity at the cutoff, find the magnitude of velocity at time t after the cutoff.

A body starts moving with a velocity v_0 = 10 ms^-1. It experiences a retardation equal to 0.2v^2. Its velocity after 2s is given by

The retardation experienced by a movign motr bat after its engine is cut-off , at the instant (t) is given by , =-k v^4 , where (k) is a constant. If v_0 is the magnitude of velocity at the cut-off , the magnitude fo velocity at time (t) after the cut-off is .

A particle moves with an initial velocity V_(0) and retardation alpha v , where alpha is a constant and v is the velocity at any time t. Velocity of particle at time is :